<h2>Problem 293</h2>
<div style="color:#666;font-size:80%;">22 May 2010</div><br />
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<p>
An even positive integer N will be called admissible, if it is a power of 2 or its distinct prime factors are consecutive primes.<br />
The first twelve admissible numbers are 2,4,6,8,12,16,18,24,30,32,36,48.
</p>
<p>
If N is admissible, the smallest integer M <img src='images/symbol_gt.gif' width='10' height='10' alt='&gt;' border='0' style='vertical-align:middle;' /> 1 such that N+M is prime, will be called the pseudo-Fortunate number for N.
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<p>
For example, N=630 is admissible since it is even and its distinct prime factors are the consecutive primes 2,3,5 and 7.<br /> 
The next prime number after 631 is 641; hence, the pseudo-Fortunate number for 630 is M=11.<br />
It can also be seen that the pseudo-Fortunate number for 16 is 3.
</p>
<p>
Find the sum of all distinct pseudo-Fortunate numbers for admissible numbers N less than 10<img src="" style="display:none;" alt="^(" /><sup>9</sup><img src="" style="display:none;" alt=")" />.
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